An Introductory Guide to Koopman Learning
Koopman operators provide a linear framework for data-driven analyses of nonlinear dynamical systems, but their infinite-dimensional nature presents major computational challenges. In this article, we offer an introductory guide to Koopman learning, emphasizing rigorously convergent data-driven methods for forecasting and spectral analysis. We provide a unified account of error control via residuals in both finite- and infinite-dimensional settings, an elementary proof of convergence for generalized Laplace analysis -- a variant of filtered power iteration that works for operators with continuous spectra and no spectral gaps -- and review state-of-the-art approaches for computing continuous spectra and spectral measures. The goal is to provide both newcomers and experts with a clear, structured overview of reliable data-driven techniques for Koopman spectral analysis.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
KoopmanFlow: Spectrally Decoupled Generative Control Policy via Koopman Structural Bias
Generative Control Policies (GCPs) show immense promise in robotic manipulation but struggle to simultaneously model stable global motions and high-frequency local corrections. While modern architectures extract multi-sc…
Robust Online Residual Refinement via Koopman-Guided Dynamics Modeling
Imitation learning (IL) enables efficient skill acquisition from demonstrations but often struggles with long-horizon tasks and high-precision control due to compounding errors. Residual policy learning offers a promisin…
Control of Oscillatory Temperature Field in a Building via Damping Assignment to Nonlinear Koopman Mode
This paper addresses a control problem on air-conditioning systems in buildings that is regarded as a control practice of nonlinear distributed-parameter systems. Specifically, we consider the design of a controller for …
Trustworthy Koopman Operator Learning: Invariance Diagnostics and Error Bounds
Koopman operator theory provides a global linear representation of nonlinear dynamics and underpins many data-driven methods. In practice, however, finite-dimensional feature spaces induced by a user-chosen dictionary ar…
How Novice Programmers Use and Experience ChatGPT when Solving Programming Exercises in an Introductory Course
This research paper contributes to the computing education research community's understanding of Generative AI (GenAI) in the context of introductory programming, and specifically, how students utilize related tools, suc…